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Orthogonal Reverse Derivations on semiprime Γ-semirings

Year 2019, Volume: 7 Issue: 1, 71 - 77, 30.04.2019
https://doi.org/10.36753/mathenot.559255

Abstract

In this paper, we introduce the notion of reverse derivation and orthogonal reverse derivations on
Γ-semirings. Some characterizations of semi prime Γ-semirings are obtained by means of orthogonal
reverse derivations. And also obtained necessary and sufficient conditions for two reverse derivations to
be orthogonal.

References

  • [1] Allen, P.J., A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21 (1969), 412-416.
  • [2] Bresar, M. and Vukman, J., On the left derivation and related mappings, Proc. Amer. Math. Soc., 10 (1990), 7-16.
  • [3] Dutta, T.K. and Kar, S., On regular ternary semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics,World Scientific, (2003) 343-355.
  • [4] Javed, M.A., Aslam, M. and Hussain, M., On derivations of prime Γ-semirings, Southeast Asian Bull. of Math., 37 (2013), 859-865.
  • [5] Lehmer, H., A ternary analogue of abelian groups, Amer. J. of Math., 59 (1932), 329-338.
  • [6] Lister, W.G., Ternary rings, Tran. of Amer. Math. Soc., 154 (1971), 37-55.
  • [7] Murali Krishna Rao, M., Γ-semirings-I, Southeast Asian Bull. of Math., 19(1) (1995), 49-54.
  • [8] Murali Krishna Rao, M., Γ-semirings-II, Southeast Asian Bull. of Math., 21 (1997), 281-287.
  • [9] Murali Krishna Rao, M. and Venkateswarlu, B., Regular Γ-semirings and field Γ-semirings, Novi Sad J. of Math., 45 (2) (2015), 155-171.
  • [10] Neumann, V., On regular rings, Proc. Nat. Acad. Sci., 22 (1936), 707-13.
  • [11] Nobusawa, N., On a generalization of the ring theory, Osaka. J. Math., 1 (1964), 81 - 89.
  • [12] Posner, E.C., Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
  • [13] Sen, M.K., On Γ-semigroup, Proc. of International Conference of algebra and its application, (1981), Decker Publicaiton, New York, 301-308.
  • [14] Suganthameena, N. and Chandramouleeswaran, M., Orthogonal derivations on semirings, Int. J. Of Cont. Math. Sci., 9 (2014), 645-651.
  • [15] Vandiver, H.S., Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math., 40 (1934), 914-921.
Year 2019, Volume: 7 Issue: 1, 71 - 77, 30.04.2019
https://doi.org/10.36753/mathenot.559255

Abstract

References

  • [1] Allen, P.J., A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21 (1969), 412-416.
  • [2] Bresar, M. and Vukman, J., On the left derivation and related mappings, Proc. Amer. Math. Soc., 10 (1990), 7-16.
  • [3] Dutta, T.K. and Kar, S., On regular ternary semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics,World Scientific, (2003) 343-355.
  • [4] Javed, M.A., Aslam, M. and Hussain, M., On derivations of prime Γ-semirings, Southeast Asian Bull. of Math., 37 (2013), 859-865.
  • [5] Lehmer, H., A ternary analogue of abelian groups, Amer. J. of Math., 59 (1932), 329-338.
  • [6] Lister, W.G., Ternary rings, Tran. of Amer. Math. Soc., 154 (1971), 37-55.
  • [7] Murali Krishna Rao, M., Γ-semirings-I, Southeast Asian Bull. of Math., 19(1) (1995), 49-54.
  • [8] Murali Krishna Rao, M., Γ-semirings-II, Southeast Asian Bull. of Math., 21 (1997), 281-287.
  • [9] Murali Krishna Rao, M. and Venkateswarlu, B., Regular Γ-semirings and field Γ-semirings, Novi Sad J. of Math., 45 (2) (2015), 155-171.
  • [10] Neumann, V., On regular rings, Proc. Nat. Acad. Sci., 22 (1936), 707-13.
  • [11] Nobusawa, N., On a generalization of the ring theory, Osaka. J. Math., 1 (1964), 81 - 89.
  • [12] Posner, E.C., Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
  • [13] Sen, M.K., On Γ-semigroup, Proc. of International Conference of algebra and its application, (1981), Decker Publicaiton, New York, 301-308.
  • [14] Suganthameena, N. and Chandramouleeswaran, M., Orthogonal derivations on semirings, Int. J. Of Cont. Math. Sci., 9 (2014), 645-651.
  • [15] Vandiver, H.S., Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math., 40 (1934), 914-921.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

B. Venkateswarlu

M. Murali Krishna Rao

Y. Adi Narayana This is me

Publication Date April 30, 2019
Submission Date January 18, 2018
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Venkateswarlu, B., Rao, M. M. K., & Narayana, Y. A. (2019). Orthogonal Reverse Derivations on semiprime Γ-semirings. Mathematical Sciences and Applications E-Notes, 7(1), 71-77. https://doi.org/10.36753/mathenot.559255
AMA Venkateswarlu B, Rao MMK, Narayana YA. Orthogonal Reverse Derivations on semiprime Γ-semirings. Math. Sci. Appl. E-Notes. April 2019;7(1):71-77. doi:10.36753/mathenot.559255
Chicago Venkateswarlu, B., M. Murali Krishna Rao, and Y. Adi Narayana. “Orthogonal Reverse Derivations on Semiprime Γ-Semirings”. Mathematical Sciences and Applications E-Notes 7, no. 1 (April 2019): 71-77. https://doi.org/10.36753/mathenot.559255.
EndNote Venkateswarlu B, Rao MMK, Narayana YA (April 1, 2019) Orthogonal Reverse Derivations on semiprime Γ-semirings. Mathematical Sciences and Applications E-Notes 7 1 71–77.
IEEE B. Venkateswarlu, M. M. K. Rao, and Y. A. Narayana, “Orthogonal Reverse Derivations on semiprime Γ-semirings”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 71–77, 2019, doi: 10.36753/mathenot.559255.
ISNAD Venkateswarlu, B. et al. “Orthogonal Reverse Derivations on Semiprime Γ-Semirings”. Mathematical Sciences and Applications E-Notes 7/1 (April 2019), 71-77. https://doi.org/10.36753/mathenot.559255.
JAMA Venkateswarlu B, Rao MMK, Narayana YA. Orthogonal Reverse Derivations on semiprime Γ-semirings. Math. Sci. Appl. E-Notes. 2019;7:71–77.
MLA Venkateswarlu, B. et al. “Orthogonal Reverse Derivations on Semiprime Γ-Semirings”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, 2019, pp. 71-77, doi:10.36753/mathenot.559255.
Vancouver Venkateswarlu B, Rao MMK, Narayana YA. Orthogonal Reverse Derivations on semiprime Γ-semirings. Math. Sci. Appl. E-Notes. 2019;7(1):71-7.

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